Predictive Lagrangian Optimization for Constrained Reinforcement Learning
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arXiv
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| Autores principales: | , , , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866929687726391296 |
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| author | Zhang, Tianqi Yuan, Puzhen Zhan, Guojian Lin, Ziyu Lyu, Yao Qin, Zhenzhi Duan, Jingliang Zhang, Liping Li, Shengbo Eben |
| author_facet | Zhang, Tianqi Yuan, Puzhen Zhan, Guojian Lin, Ziyu Lyu, Yao Qin, Zhenzhi Duan, Jingliang Zhang, Liping Li, Shengbo Eben |
| contents | Constrained optimization is popularly seen in reinforcement learning for addressing complex control tasks. From the perspective of dynamic system, iteratively solving a constrained optimization problem can be framed as the temporal evolution of a feedback control system. Classical constrained optimization methods, such as penalty and Lagrangian approaches, inherently use proportional and integral feedback controllers. In this paper, we propose a more generic equivalence framework to build the connection between constrained optimization and feedback control system, for the purpose of developing more effective constrained RL algorithms. Firstly, we define that each step of the system evolution determines the Lagrange multiplier by solving a multiplier feedback optimal control problem (MFOCP). In this problem, the control input is multiplier, the state is policy parameters, the dynamics is described by policy gradient descent, and the objective is to minimize constraint violations. Then, we introduce a multiplier guided policy learning (MGPL) module to perform policy parameters updating. And we prove that the resulting optimal policy, achieved through alternating MFOCP and MGPL, aligns with the solution of the primal constrained RL problem, thereby establishing our equivalence framework. Furthermore, we point out that the existing PID Lagrangian is merely one special case within our framework that utilizes a PID controller. We also accommodate the integration of other various feedback controllers, thereby facilitating the development of new algorithms. As a representative, we employ model predictive control (MPC) as the feedback controller and consequently propose a new algorithm called predictive Lagrangian optimization (PLO). Numerical experiments demonstrate its superiority over the PID Lagrangian method, achieving a larger feasible region up to 7.2% and a comparable average reward. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15217 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Predictive Lagrangian Optimization for Constrained Reinforcement Learning Zhang, Tianqi Yuan, Puzhen Zhan, Guojian Lin, Ziyu Lyu, Yao Qin, Zhenzhi Duan, Jingliang Zhang, Liping Li, Shengbo Eben Machine Learning Systems and Control Constrained optimization is popularly seen in reinforcement learning for addressing complex control tasks. From the perspective of dynamic system, iteratively solving a constrained optimization problem can be framed as the temporal evolution of a feedback control system. Classical constrained optimization methods, such as penalty and Lagrangian approaches, inherently use proportional and integral feedback controllers. In this paper, we propose a more generic equivalence framework to build the connection between constrained optimization and feedback control system, for the purpose of developing more effective constrained RL algorithms. Firstly, we define that each step of the system evolution determines the Lagrange multiplier by solving a multiplier feedback optimal control problem (MFOCP). In this problem, the control input is multiplier, the state is policy parameters, the dynamics is described by policy gradient descent, and the objective is to minimize constraint violations. Then, we introduce a multiplier guided policy learning (MGPL) module to perform policy parameters updating. And we prove that the resulting optimal policy, achieved through alternating MFOCP and MGPL, aligns with the solution of the primal constrained RL problem, thereby establishing our equivalence framework. Furthermore, we point out that the existing PID Lagrangian is merely one special case within our framework that utilizes a PID controller. We also accommodate the integration of other various feedback controllers, thereby facilitating the development of new algorithms. As a representative, we employ model predictive control (MPC) as the feedback controller and consequently propose a new algorithm called predictive Lagrangian optimization (PLO). Numerical experiments demonstrate its superiority over the PID Lagrangian method, achieving a larger feasible region up to 7.2% and a comparable average reward. |
| title | Predictive Lagrangian Optimization for Constrained Reinforcement Learning |
| topic | Machine Learning Systems and Control |
| url | https://arxiv.org/abs/2501.15217 |